A large hotel finds that it can rent 95 rooms when it charge $100 per room. For each $1 increase in room cost it rents one room less. (Likewise, for each $1 decrease in room cost it rents one room more)

What price should it charge in order to maximize the revenue?

if there are x price increases, the revenue is

(95-x)(100+x)

That is just a parabola. Its vertex represents maximum revenue.

To find the price at which the hotel can maximize its revenue, we need to understand the relationship between room price and the number of rooms rented.

According to the given information, when the hotel charges $100 per room, it can rent 95 rooms. With each $1 increase in room cost, it rents one room less, and with each $1 decrease in room cost, it rents one room more.

We can set up a table to illustrate this relationship:

Room Cost (Price) | Number of Rooms Rented
----------------------------------------
$100 | 95
$99 | 96
$98 | 97
$97 | 98
$96 | 99
$95 | 100

From the table, as the room cost decreases, the number of rooms rented increases, and vice versa.

To calculate the revenue for each combination of price and number of rooms rented, we multiply the room cost by the number of rooms rented.

Revenue = Room Cost * Number of Rooms Rented

Let's calculate the revenue for each row in the table:

Revenue at $100 = $100 * 95 = $9,500
Revenue at $99 = $99 * 96 = $9,504
Revenue at $98 = $98 * 97 = $9,506
Revenue at $97 = $97 * 98 = $9,506
Revenue at $96 = $96 * 99 = $9,504
Revenue at $95 = $95 * 100 = $9,500

From the calculations, we can observe that the revenue is highest at $9,506, which occurs when the hotel charges either $98 or $97 per room.

Therefore, to maximize its revenue, the hotel should charge either $98 or $97 per room.